Solve for $p$, $ -\dfrac{1}{p + 2} = -\dfrac{7}{4p + 8} + \dfrac{5p - 6}{4p + 8} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $p + 2$ $4p + 8$ and $4p + 8$ The common denominator is $4p + 8$ To get $4p + 8$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{1}{p + 2} \times \dfrac{4}{4} = -\dfrac{4}{4p + 8} $ The denominator of the second term is already $4p + 8$ , so we don't need to change it. The denominator of the third term is already $4p + 8$ , so we don't need to change it. This give us: $ -\dfrac{4}{4p + 8} = -\dfrac{7}{4p + 8} + \dfrac{5p - 6}{4p + 8} $ If we multiply both sides of the equation by $4p + 8$ , we get: $ -4 = -7 + 5p - 6$ $ -4 = 5p - 13$ $ 9 = 5p $ $ p = \dfrac{9}{5}$